The parameter \(T_{\mathrm {lim}}\)  defines the plateau in temperature for high beam energies observed in experiment (see cf. Fig.  REF ).
Other definitions of a universal freeze-out line assume fixed energy per particle or constant entropy density etc. [1]}.
Using the above parameterization (Eqs. REF  and REF ), the particle multiplicity densities \(n_i\)  in central collisions can be calculated for a given collision energy using the approximate formula [2]}
\(\nonumber n_i \left( T,\lbrace  \mu \rbrace  \right) & = &\frac{g_i T^3}{2\pi ^2}\sum _{n=1}^{\infty }\frac{\left( \pm \lambda _i \right)^n}{n^3}\left(\frac{n m_i}{T}\right)^2K_2\left( \frac{n m_i}{T} \right)\\& = &\frac{g_i \lambda _i}{2\pi ^2}m_i^2 T K_2\left( \frac{m_i}{T} \right) \pm \mathrm {h.o.}\: .\) 
